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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 2450.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.p1 | 2450b2 | \([1, 1, 0, -12275, -528625]\) | \(-5452947409/250\) | \(-9378906250\) | \([]\) | \(4320\) | \(0.98911\) | |
2450.p2 | 2450b1 | \([1, 1, 0, -25, -1875]\) | \(-49/40\) | \(-1500625000\) | \([]\) | \(1440\) | \(0.43980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.p have rank \(1\).
Complex multiplication
The elliptic curves in class 2450.p do not have complex multiplication.Modular form 2450.2.a.p
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.